Zobrazeno 1 - 10
of 94
pro vyhledávání: '"60E"'
Autor:
Bobkov, Sergey, Götze, Friedrich
Berry-Esseen-type bounds are developed in the multidimensional local limit theorem in terms of the Lyapunov coefficients and maxima of involved densities.
Externí odkaz:
http://arxiv.org/abs/2407.20744
Autor:
Bobkov, Sergey, Götze, Friedrich
The paper is devoted to the investigation of Esscher's transform on high dimensional Euclidean spaces in the light of its application to the central limit theorem. With this tool, we explore necessary and sufficient conditions of normal approximation
Externí odkaz:
http://arxiv.org/abs/2407.20726
We show several variants of concentration inequalities on the sphere stated as subgaussian estimates with optimal constants. For a Lipschitz function, we give one-sided and two-sided bounds for deviation from the median as well as from the mean. For
Externí odkaz:
http://arxiv.org/abs/2406.13581
Autor:
Bobkov, Sergey G., Götze, Friedrich
For normalized sums $Z_n$ of i.i.d. random variables, we explore necessary and sufficient conditions which guarantee the normal approximation with respect to the R\'enyi divergence of infinite order. In terms of densities $p_n$ of $Z_n$, this is a st
Externí odkaz:
http://arxiv.org/abs/2402.02259
Lower and upper bounds are explored for the uniform (Kolmogorov) and $L^2$-distances between the distributions of weighted sums of dependent summands and the normal law. The results are illustrated for several classes of random variables whose joint
Externí odkaz:
http://arxiv.org/abs/2308.02693
We explore the class of probability distributions on the real line whose Laplace transform admits a strong upper bound of subgaussian type. Using Hadamard's factorization theorem, we extend the class $\mathfrak L$ of Newman and propose new sufficient
Externí odkaz:
http://arxiv.org/abs/2308.01749
Autor:
Arnold, Barry C., Ghosh, Indranil
Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics, etc., to name but a few) and the bivariate Poisson distribution which is a generalization of the Poisson distribution plays an important role in
Externí odkaz:
http://arxiv.org/abs/2301.04251
In this article, we discuss a bivariate distribution whose conditionals are univariate binomial distributions and the marginals are not binomial that exhibits negative correlation. Some useful structural properties of this distribution namely margina
Externí odkaz:
http://arxiv.org/abs/2301.03087
Publikováno v:
Lith Math J, 63, 138 - 160, 2023
We give a detailed exposition of the proof of Richter's local limit theorem in a refined form, and establish the stability of the remainder term in this theorem under small perturbations of the underlying distribution (including smoothing). We also d
Externí odkaz:
http://arxiv.org/abs/2208.09534
Publikováno v:
Lithuanian Mathematical Journal 63 (2023), 1-12
In probability theory, there exist discrete and continuous distributions. Generally speaking, we do not have sufficient kinds and properties of discrete ones compared to the continuous ones. In this paper, we treat the Riemann zeta distribution as a
Externí odkaz:
http://arxiv.org/abs/2201.13397